6533b834fe1ef96bd129ccd1
RESEARCH PRODUCT
Non-accumulation of critical points of the Poincaré time on hyperbolic polycycles
Mariana SaavedraPavao Mardešićsubject
Critical period; finiteness; non-accumulation; quasi-analyticity; Dulac problem.Applied MathematicsGeneral MathematicsLimit cycleMathematical analysisHyperbolic manifoldPrincipal partUltraparallel theoremVector fieldRelatively hyperbolic groupCritical point (mathematics)Hyperbolic equilibrium pointMathematicsdescription
We call Poincare time the time associated to the Poincar6 (or first return) map of a vector field. In this paper we prove the non-accumulation of isolated critical points of the Poincare time T on hyperbolic polycycles of polynomial vector fields. The result is obtained by proving that the Poincare time of a hyperbolic polycycle either has an unbounded principal part or is an almost regular function. The result relies heavily on the proof of Il'yashenko's theorem on non-accumulation of limit cycles on hyperbolic polycycles.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-06-22 | Proceedings of the American Mathematical Society |